UMHS Keystone review: Module 1

A1.1.1.1.1

Compare and/or order any real numbers.

Note: Rational and irrational may be mixed.

1. Which of the following inequalities is true for all

real values of x?

A.	C.
B. (2x)^23x^2	D.

2. Which of the following represents the greatest 

    value?

A.	C.
B.	D.

3. If you were to order the real numbers below

    from the largest to the smallest, which real

    number would be the third in your list?

A. -5

B. -5.5

C.

D.

4. Compare the two absolute value expressions           
     and choose the statement below that is true.

       Expression 1:

       Expression 2: 

      a.  Expression 1 is greater than Expression 2.

      b.  Expression 2 is greater than Expression 1.

      c.  The expressions are equal.

      d.  There is not enough information for a 

           comparison.

5.  Four numbers are shown.

Which shows these numbers ordered from

     least to greatest?

A.	C.
B.	D.

6.  When , which expression has a value less

     than ?

A.

B.

C.

D.

7.  Which sequence of numerals is equivalent to:

A.	C.
B.	D.

A1.1.1.1.2

Simplify square roots

8. An expression is shown below.

    Which value of x makes the expression   

    equivalent to ?

A. 5

B. 25

C. 50

D. 100

9. An expression is shown below.

    For which value of x should the expression be 

    further simplified?

A. x = 10

B. x = 13

C. x = 21

D. x = 38

10. Which expression is equivalent to ?

A.

B.

C.

D.

11. Which number equals  ?

A.

B.

C.

D.

12.  On the number line, point R represents the

       square root of a number.

       Which value could be the square root of the

       number represented by R?

A. 137

B. 149

C. 165

D. 173

A1.1.1.2.1

Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.

13. Two monomials are shown below.

450x²y⁵     3,000x⁴y³

       What is the least common multiple (LCM) of

       these monomials?

A.  2xy	C.
B. 30xy	D.

14. Which expression is the greatest common

      factor of

?

A.

B.

C.

D.

15. Which of the following is equivalent to 

?

A.	C.
B.	D.

A1.1.1.3.1

Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems.

Note: Exponents should be integers from -10 to 10.

16. Simplify 

A.

B.

C. 16

D. 32

17. Which expression is the same as  ?

A.

B.

C.

D.

18.  Which expression is the correct simplification

       of  ?

A. 0

B.

C.  1

D.

A1.1.1.4.1

Use estimation to solve problems.

19. A theme park charges $52 for a day pass and

      $110 for a week pass. Last month, 4,432 day

      passes were sold and 979 week passes were

      sold. Which is the closest estimate of the

      total amount of money paid for the day and

      week passes for last month?

A.  $300,000	C. $500,000
B. $400,000	D. $600,000

20. Joel has a 50-meter roll of copper wire that

      weighs 7.5 kilograms. Approximately how

      many meters of wire will be in a new shipment

      that weighs 502.5 kilograms?

A.  75 m	C. 3,350 m
B. 610 m	D. 3,770 m

A1.1.1.5.1

Add, subtract, and/or multiply polynomial expressions (express answers in simplest form).

Note: Nothing larger than a binomial multiplied by a trinomial.

21. A polynomial expression is shown below.

      The expression is simplified to

.

     What is the value of m?

A.  -8

B.  -4

C. 4

D. 8

22. Simplify

A.	C.
B.	D.

23. What polynomial equals   (x + 6)(2x – 3)?

A.	C.
B.	D.

24. The sum of  and

 is

A. 

B.

C.

D.

A1.1.1.5.2

Factor algebraic expressions, including difference of squares and trinomials.

Note: Trinomials are limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors.

25. When the expression is factored

      completely, which is one of its factors?

A. (x – 2)

B. (x – 3)

C. (x – 6)

D. (x – 9)

26. Which expression is a factor of ?

A. 2(x+3)	C. 4(x+3)
B. 2x+3	D. 4x+3

27. Which expression represents in

      simplest factored form?

A.

B.

C.

D.

28. Which of the following is a factor of

?

A. x + 1

B. 2x – 1

C. 3x + 1

D. 6x - 1

A1.1.1.5.3

Simplify/reduce a rational algebraic expression.

29. Simplify   ; x -4, -2, 0

A.	C.
B.	D.

30. What is the sum of  and ?

A.	C.
B.	D.

31. When the following expression is simplified,

      what is the numerator?

A. 3(x+1)	C. 3(2x + 3)
B. 3(x + 3)	D. 3(x + 3)

A1.1.2.1.1

Write, solve, and/or apply a linear equation (including problem situations).

32. Mr. and Mrs. Rodriguez are taking their

      children to Colonial Williamsburg. A 1-day

      admission pass is $33 for an adult and $16.50

      for a child. If they pay a total of $115.50

      admission for themselves and their children,

      how many children do they have?

A. 2

B. 3

C. 4

D. 5

33. Luigi earns $8 per hour baby-sitting and $10

      per hour working at a movie theater. If he

      baby-sits 50 hours in a year, how many hours

      would he need to work at the theater in order

      to earn $3,000 for a computer? Which

      equation represents this situation where x is

      the number of hours he would need to work at

      the theater?

A. 400 + 10x = 3,000	C. 8x + 10x = 3,000
B. 500 + 8x = 3,000	D. 10x =  3,400

34. A taxi ride cost $29.40. The driver charged $3

      plus $0.40 per 0.2 mile traveled. How far did

      the taxi travel on this trip?

A. 9.8 mi

B.13.2 mi

C. 66 mi

D.73.5 mi

35. Which of the following equations has an infinite number of solutions? 

A.	C.
B.	D.

36.  Michael paid $6.00 for a ticket to a football

       game. Soft drinks at the game cost $0.75.

       Michael bought x drinks at the game. Which

       equation represents the total amount(y)

       he spent?

A. y = (6 + 0.75)x	C. y = 6 – 0.75x
B. y = 6x + 0.75	D. y = 6 + 0.75x

A1.1.2.1.2

Use and/or identify an algebraic property to justify any step in an equation-solving process.

Note: Linear equations only.

37. Stan’s solution to an equation is shown   
      below.

          Given: n+8( n+20) =110

          Step 1:    n+8n+20 =110

          Step 2:        9n+20 =110

            Step 3:               9n=110 −20

            Step 4:               9n=90

            Step 5:            

            Step 6:                 n=10

     Which statement about Stan’s solution is true?

       A. Stan’s solution is correct

       B. Stan made a mistake in step 1

       C. Stan made a mistake in step 3

       D. Stan made a mistake in step 5

38. One of the steps Jamie used to solve an

       equation is shown below.

–5(3x + 7) = 10

–15x + –35 = 10

       Which statements describe the procedure

       Jamie used in this step and identify the

       property that justifies the procedure?

         A. Jamie added –5 and 3x to eliminate the parentheses.

              This procedure is justified by the associative property.

          B. Jamie added –5 and 3x to eliminate the parentheses.

              This procedure is justified by the distributive property.

          C. Jamie multiplied 3x and 7 by –5 to eliminate the

              parentheses. This procedure is justified by the

              associative property.

          D. Jamie multiplied 3x and 7 by –5 to eliminate the

              parentheses. This procedure is justified by the 

              distributive property.

39. Solve  3(x+5) = 2x + 35

        Step 1:            3x + 15 = 2x + 35

        Step 2:            5x + 15 = 35

        Step 3:                    5x = 20

        Step 4:                      x = 4

       Which is the first incorrect step in the solution

       shown above?

A. Step 1

B. Step 2

C. Step 3

D. Step 4

A1.1.2.1.3

Interpret solutions to problems in the context of the problem situation.

Note: Linear equations only.

40. Francisco purchased x hot dogs and y

hamburgers at a baseball game. He spent a

      total of $10. The equation below describes the

      relationship between the number of hot dogs

      and the number of hamburgers purchased.

3x + 4y = 10

      The ordered pair (2, 1) is a solution of the   

      equation.  What does the solution (2, 1)

      represent?

A. Hamburgers cost 2 times as much as hot dogs.

B. Francisco purchased 2 hot dogs & 1 hamburger.

C. Hot dogs cost $2 each & hamburgers cost $1

     each.

D. Francisco spent $2 on hot dogs & $1 on

     hamburgers.

41. The data in the table show the cost of renting

      a bicycle by the hour, including a deposit.

      The equation of the line that fits the data is

      c = 5h + 5.  An ordered pair that is a solution

      to the equation is (3 , 20).  What does that

      solution represent?

A. The deposit for renting the bicycle for 3 hours is

     $20.

B. The cost is $20 to rent a bicycle for 3 hours.

C. The deposit is $3 when the total cost is $20

D. The cost is $3 for renting a bicycle for 20 hours

42. Marcy and Troy disagreed about the answer to a problem. Marcy said that the equation they were working on had more than one solution. If Marcy is correct, on which of these equations could they have been working?

A. 2x + 4 = 3x + 4	C. 2x + 4 = 2(x + 2)
B. 2x + 4 = 3x + 5	D. 2x + 4 = 2(x + 3)

43.  Which of the following is not a correct

       description of the graph of the function

y = −2x − 7?

A The graph of the function contains the point (−2, −3),

and when the value of x increases by 1 unit, the

    value of y decreases by 2 units.

B The graph of the function contains the points

    (−1, −5), (2, −11), and (4, −15).

C The graph of the function is a line that passes

    through the point (0, −7) with a slope of −2.

D The graph of the function contains the points (0, −7),

    (1, −9), and (3, −1).

A1.1.2.2.1

Write and/or solve a system of linear equations (including problem situations) using  graphing, substitution, and/or elimination.

Note: Limit systems to two linear equations.

44. Adult tickets to a museum cost $10 while

      children’s tickets cost $6. Suppose that at the

      end of one day the museum had sold 5,000

      tickets and had received  $42,000 in

      admission fees.

      Which system of equations could represent

      this situation if x is the number of adult’s

      tickets sold and y the number of children’s

      tickets sold?

A.	C.
B.	D.

45. Rosilita paid $10.85 for 3 loaves of bread and

      2 gallons of milk. A gallon of milk costs $0.91

      more than twice the cost of a loaf of bread.

      Which equation could Rosilita use to find the

      cost x of one loaf of bread?

A.

B.

C.

D.

46. Anna burned 15 calories per minute running

      for x minutes and 10 calories per minute hiking

      for y minutes. She spent a total of 60 minutes

      running and hiking and burned 700 calories.

      The system of equations shown below can be

      used to determine how much time Anna spent

      on each exercise.

15x + 10y = 700

x + y = 60

      What is the value of x, the minutes Anna spent

      running?

A. 10

B. 20

C. 30

D. 40

47. If ( x, y) is the solution to the system of

      equation,  y= 2x – 4 and y = x + 1, what is

?

A. -21

B. -19

C. 19

D. -31

48. Edith is using substitution to solve the system

      of equations below.  What should the first step

      be?  Choose the correct first step from the

      choices below.

A.	C.
B.	D.

49. A company is comparing two different postage

      plans for next year. The company can

      purchase a postage plan where the total cost,

c₁, is $45,000 plus $3,000 per mailing, where

n is the number of mailings. The cost, c₂, of  

      the other plan is $0.35 for each piece, p,

      mailed. Which of the following is a set of

      equations modeling the costs of the two

      plans?

A. c₁ = 45000n + 3000

    c₂ = 0.035p

B. c₁ = 45000 + 3000n

    c₂ = 0.35 + p

C. c₁ = 45000n + 3000

    c₂ = 0.35 + p

D. c₁ = 45000 + 3000n

    c₂ = 0.35p

50. Southern Phone Company is promoting a new

      cell phone service plan: a customer can make

      up to 500 minutes of calls each month for

      $39.99. If the number of minutes used in a

      month exceeds 500, then the function

c_І = 0.40(m − 500) + 39.99

describes the monthly charge, c, in dollars in terms of m, the total number of minutes used. Which of the following statements best describes this function?

A. A.  If the total number of minutes used is more than 500,   
      then every minute beyond 500 costs 40 cents.

B.  Every minute used costs 40 cents, regardless of the

      total number of minutes used.

C.  The first 500 minutes used costs 40 cents each, after  

      which there is an additional charge of $39.99.

D.  If the total number of minutes used is more than 500,

      then every minute used costs 40 cents.

51.  The sum of the perimeters of two different squares

       is 32 cm, and the difference between their

       perimeters is 8 cm.  If x represents the side length

       of the larger square and y represents the side length

       of the smaller square, which of the following

       systems of equations could be used to find the

       dimensions of the squares?

A.	C.
B.	D.

A1.1.2.2.2

Interpret solutions to problems in the context of the problem situation.

Note: Limit systems to two linear equations.

52. Which description best compares the graphs

      given by the equations:

-6x + 15y = 5    and    30x + 12y = 4?

A. Parallel

B. Coincident

C. Perpendicular

D. Intersecting but not perpendicular

53. A salesman rents a car for two trips from the

      same rental company. The rental company

      charges a daily fee plus a charge for each mile

      driven.

Trip	Time	Distance Traveled	Cost
First Trip	2 Days	275 Miles	$140.75
Second Trip	1 Day	95 Miles	$59.75

      According to this table, how much did the

      rental company charge per day and per mile?

A.  $17 per day and $0.45 per mile

B.  $36 per day and $0.25 per mile

C.  $8.45 per day and $0.54 per mile

D.  $70.38 per day and $0.63 per mile

54. Samantha and Maria purchased flowers.

      Samantha purchased 5 roses for x dollars

      each and 4 daisies for y dollars each and

      spent $32 on the flowers. 

      Maria purchased 1 rose for x dollars and 6

      daisies for y dollars each and spent $22. The

      system of equations shown below represents

      this situation.

5x + 4y = 32

x + 6y = 22

      Which statement is true?

A. A rose costs $1 more than a daisy.

B. Samantha spent $4 on each daisy.

C. Samantha spent more on daisies than she did on

     roses.

D. Samantha spent over 4 times as much on daisies

     as she did on roses.

55. Consider the system of equations below.

      Which statement correctly describes the

      graphs of these equations?

A. The lines are parallel.

B. The lines coincide.

C. The lines intersect at (2, 4)

D. The lines intersect at (−2, 8).

A1.1.3.1.1

Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

56. Choose the inequality below that matches the

      solution represented on the number line

      shown.

A.	C.
B.	D.

A1.1.3.1.2

Identify or graph the solution set to a linear inequality on a number line.

57. The solution set of an inequality is graphed on

      the number line below.

      The graph shows the solution set of which

      inequality?

A. 2x + 5 < –1	C. 2x + 5 > –1
B. 2x + 5 ≤ –1	D. 2x + 5 ≥ –1

58. Which number line displays the solution set of

      the inequality: 

A.	C.
B.	D.

59. How many solutions does an inequality like 

 have?

A. One

B. Two

C. Infinite

. None

60. Consider the inequality  6x + y < p

      What must be true about the value of p in

       order for the origin to be part of the solution?

A.

B.

C.

D.

A1.1.3.1.3

Interpret solutions to problems in the context of the problem situation.

Note: Limit to linear inequalities.

61. A baseball team had $1,000 to spend on

      supplies. The team spent $185 on a new bat.

      New baseballs cost $4 each. The inequality

      185 + 4b ≤ 1,000 can be used to determine

      the number of new baseballs (b) that the team

      can purchase. Which statement about the

      number of new baseballs that can be

      purchased is true?

A. The team can purchase 204 new baseballs.

B. The minimum number of new baseballs that can

     be purchased is 185.

C. The maximum number of new baseballs that can

     be purchased is 185.

D. The team can purchase 185 new baseballs, but

     this number is neither the maximum nor the

     minimum.

A1.1.3.2.1

Write and/or solve a system of linear inequalities using graphing.

Note: Limit systems to two linear inequalities.

62.  A system of inequalities is shown below.

      Which graph shows the solution set of the

      system of inequalities?

A.	C.
B.	D.

63.  Which graph best represents the solution to

       the system of linear inequalities?

A.	C.
B.	D.

A1.1.3.2.2

Interpret solutions to problems in the context of the problem situation.

Note: Limit systems to two linear inequalities.

64. Tyreke always leaves a tip of between 8%

       and 20% for the server when he pays for his

       dinner. This can be represented by the

       system of inequalities shown below, where y

is the amount of tip and x is the cost of dinner.

y > 0.08x

y < 0.2x

       Which of the following is a true statement?

A. When the cost of dinner (x) is $10, the amount of

    tip (y) must be between $2 and $8.

B. When the cost of dinner (x) is $15, the amount of

    tip (y) must be between $1.20 and $3.00.

C. When the amount of tip (y) is $3, the cost of

    dinner (x) must be between $11 and $23.

D. When the amount of tip (y) is $2.40, the cost of 

    dinner (x) must be between $3 and $6.

Answers:

1.	C	33.	A
2.	C	34.	B
3.	A	35.	D
4.	A	36.	D
5.	C	37.	B
6.	C	38.	D
7.	C	39.	B
8.	B	40.	B
9.	C	41.	B
10.	B	42.	C
11.	A	43.	C
12.	B	44.	C
13.	D	45.	D
14.	A	46.	B
15.	B	47.	D
16.	A	48.	A
17.	C	49.	D
18.	C	50.	A
19.	A	51.	B
20.	C	52.	C
21.	C	53.	B
22.	D	54.	A
23.	A	55.	A
24.	C	56.	B
25.	C	57.	D
26.	B	58.	C
27.	C	59.	C
28.	B	60.	D
29.	D	61.	D
30.	B	62.	A
31.	D	63.	D
32.	B	64.	B